The new era in intergovernmental relations promised by President Carter dawned almost unnoticed the other day at a breakfast in the public dining room of the Hay-Adams Hotel.

Present were lobbyists for the major state, city and county organizations who like to refer to themselves as the big seven." The speaker was Carter aide Jack H. Watson, who was praised for his candor, openness and what one of the lobbyists called the best smile since Aunt Jemima."

But Watson had scarely left the breakfast gathering before lobbyists were asking themselves and each other the question uppermost on their minds: are intergovernmental relations going to by any different under President Carter than they have been in the past?

Certainly, Carter has promised that they will be different. He pledged during the campaign to restore a true system of federalism" to the nation and said he would learn from his own dealinss with the federal government when he was governor of Georgia. State and local government representatives consider Carter to be understanding of the complex problems in dealing with the federal establishment.

This mutual goodwill may not be enough to overcome the manifold problems facing the Carter administration in its efforts to establish a new system of intergovernmental relationships. Already, the diverse elements of the broad coalition of state and local government lobbyists are voicing skepticism.

One of the reasons for the skepticism is that Carter's promises at this point appear to be somewhat in conflict. The President has said that he favors "targeting" so that federal funds will go to the government agencies and the people who need them most. But, remembering the strings on federal aid that came to Georgia, he has also talked about greater flexibility for state and local governments in administering programs.

Some of the government lobbyists regard these concepts of "targeting" and "flexibility" as being inherently in conflict. Others, like John Gunther, executive director of the U.S. Conference of Mayors, believe that it is extremely difficult politically to target funds to solve hard-core unemployment when there is lots of other unemployment as well.

It's difficult to earmark money for programs that are supposed to employ people who have never had a job when there are people who have been working regularly who are now unemployed," says Gunther. Carter understands the problem, but I don't think that he or we have devised a means of solving it."

One of the difficulties confronting Watson and his aides as they attempt to define Carter's true system of federalism" is that the different elements of the state and local government coalition have different priorities.

The conference of mayors, for instance, which represents big cities with big problems, is most insistent on "targeting," while the National League of Cities, which represents thousands of medium-sized and smaller cities, generally prefers broad-based formulas. States and counties tend to emphasize changes in the welfare system and simplification of federal regulations. County goverments, which are virtually nonexistent in some regions and which administer a vast array of service programs in others, frequently regard themselves as neglected or ignored by the federal government.

The difficulty of devising a program that satisfies the conflicting requests of the states and cities is illustrated by the issue of development banks. The northeast governors want a Northeast Development Bank, the mayors want an Urban Development Bank and the National Association of Housing and Redevelopment Officials desires a bank for building development projects.

To some degree all of these seemingly good proposals are enemies of each other. The Carter administration has not yet come up with a development bank plan of its own, and any proposal in this area is likely to have more critics than advocates.

Other administration proposals, while desirable in themselves, may damage the federalism that Carter seeks to improve.

In this regard some of the mayors are worried about the investment credit in Carter's economic package, which they see as an encouragement for businesses to build new modern plants in the suburbs rather than remodel old, rundown factories in the inner city.

Both the cities and counties believe Carter's proposed two-year $31 billion economic package is too heavily weighted toward tax cuts and insufficiently directed toward public works and job creation-programs in the cities. The local government lobbyists have informed Watson and his deputies that they will fight to expand the spending portions of the economic package as the legislation proceeds through Congress.

Some of the local government lobbyists also are worried about Carter's organization of White House intergovernment relations.

In the beginning, at least, these relations will be supervised by Watson, who has the responsibility for implementing existing federal programs and by Stuart E. Eizenstat, who has the responsibility for developing legislation affecting local government. Both Carter aides also have other duties. Watson as Cabinet secretary and Eizenstat as assistant for domestic policy.

Jerry Sohns of the National Council of State Legislatures, one of the lobbyists attending the breakfast Wednesday, expressed concern that too much of Watson's time may be consumed by Cabinet duties to the exclusion of intergovernmental relations.

In the opinion of Watson deputy Bruce Kirshenbaum, the dual responsibility is a potential advantage for state and local governments because it will make sure that their concerns are voiced within the Cabinet, which Carter says will have a principal operating role in his administration.

Most of the lobbyists are favorably impressed with the qualifications of Watson and his small staff. Watson, a lawyer, was director of the Georgia department of human resources, the state's largest department. Kirshenbaum is a former lobbyist for New York City and played a major role in negotiations during the Ford administration to aid that fiscally embattled city. Another deputy, Lawrence Bailey, formerly worked for the U.S. Conference of Mayors.

They also are impressed with the Carter administration's initial policy of consulting state and local government. Steve Farber, director of the National Governors Conference, observed that the states were consulted before Carter submitted natural gas legislation to Congress.

Health, Education and Welfare Secretary Joseph A. Califano Jr. included Gov. Reubin Askew of Florida, representing the new coalition of state, city and county lobbyists, on the consulting group that will recommend changes in the welfare system.

"The executive branch of the federal government, acting alone, cannot and should not attempt to devise a program that must receive wide acceptance if it is to succeed," Califano said.

It is this wide acceptance which Watson also seeks as Carter attempts to keep his promise to improve the federal system.

"We're not going to dissolve the differences," Watson said. "But we can blunt the sharp edges of opposition by consulting with everyone and seeing that the viewpoints of state and local government are truly heard."